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Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1051
GPA: 3.39
The inside dimensions of a rectangular wooden box are 6 inches by 8 in
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05 Nov 2021, 07:02
05 Nov 2021, 07:02
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The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in
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08 Nov 2021, 14:05
08 Nov 2021, 14:05
Expert Reply
\(volume_{cylinder}=\pi{r^2}h\)
If the cylinder is placed on 6*8 face then it's maximum radius is 6/2=3 and \(volume==\pi*{3^2}*10=90\pi\);
If the cylinder is placed on 6*10 face then it's maximum radius is 6/2=3 and \(volume==\pi*{3^2}*8=72\pi\);
If the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and \(volume==\pi*{4^2}*6=96\pi\);
So, the maximum volume is for \(r=4\).
Answer: B.
If the cylinder is placed on 6*8 face then it's maximum radius is 6/2=3 and \(volume==\pi*{3^2}*10=90\pi\);
If the cylinder is placed on 6*10 face then it's maximum radius is 6/2=3 and \(volume==\pi*{3^2}*8=72\pi\);
If the cylinder is placed on 8*10 face then it's maximum radius is 8/2=4 and \(volume==\pi*{4^2}*6=96\pi\);
So, the maximum volume is for \(r=4\).
Answer: B.
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Re: The inside dimensions of a rectangular wooden box are 6 inches by 8 in
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14 Nov 2021, 11:03
14 Nov 2021, 11:03
1
GeminiHeat wrote:
The inside dimensions of a rectangular wooden box are 6 inches by 8 inches by 10 inches. A cylindrical canister is to be placed inside the box so that it stands upright when the closed box rests on one of its six faces. Of all such canisters that could be used, what is the radius, in inches, of the one that has the maximum volume?
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
(A) 3
(B) 4
(C) 5
(D) 6
(E) 8
Volume of cylinder = pi(radius²)(height)
There are 3 different ways to position the cylinder (with the base on a different side each time).
You can place the flat BASE of the cylinder on the 6x8 side, on the 6x10 side, or on the 8x10 side
If you place the base on the 6x8 side, then the cylinder will have height 10, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6).
So, the volume of this cylinder will be (pi)(3²)(10), which equals 90(pi)
If you place the base on the 6X10 side, then the cylinder will have height 8, and the maximum radius of the cylinder will be 3 (i.e., diameter of 6).
So, the volume of this cylinder will be (pi)(3²)(8), which equals 72(pi)
If you place the base on the 8x10 side, then the cylinder will have height 6, and the maximum radius of the cylinder will be 4 (i.e., diameter of 8).
So, the volume of this cylinder will be (pi)(4²)(6), which equals 96(pi)
So, the greatest possible volume is 96(pi) and this occurs when the radius is 4
Answer: B
Cheers,
Brent
